3. Interest Rates and Bond Valuation

Question 1

What is a “bond”?

Answer 1

Security that obligates the issuer to make specified payments to the bondholder

Question 2

What is a “face value”?

Answer 2

Payment at the maturity of the bond

Question 3

What is a “coupon”?

Answer 3

The interest payments made to the bondholder

Question 4

What is a “coupon rate”?

Answer 4

Annual interest payment, as a percentage of face value

Question 5

Are the interest rates on bonds the same as the opportunity cost of capital for investors?

Answer 5

Do not confuse the interest rate on bonds with the cost of capital for a corporation. The projects that companies undertake are almost invariably risky, and investors demand higher prospective returns from such projects than from safe government bonds.

Question 6

what is the PV Formula to Value a Bond?

Answer 6

where: “cpn” is an abbreviation for coupon
and where “par”: is an abbreviation for principal // face value

Question 7

Example:

Purchase a french government bod of 100 face value, with coupon payments of 3.5% every year. Suppose similar government bonds provide a 5% interest rate

What is the PV?

Answer 7

So,
cpn = 3.5% (so 3.5 in the case of a 100 face value)
r = 5% -> 0.05

Hence, the price of the 3.5%, 6 year bond would be listed as 92.39%
-> usually expressed as a percentage of face value

Question 8

What is the “yield to maturity (YTM)”?

Answer 8

YTM stand for “Yield To Maturity” and means the expected annual rate of return earned on a bond assuming the debt security is held until maturity.

Question 9

How do you calculate YTM?

Answer 9

You can only calculate the YTM through a process of trial and error (so keep trying until PV is correct)

Question 10

What do you call a bond that is priced below its face value?

Answer 10

A bond that is priced below its face value is said to sell at a discount and is known as a discount bond

Question 11

What do you call a bond that is priced above its face value?

Answer 11

A bond that sells at a premium to its face value is said to be sold at a premium and is thus known as a premium bond

Question 12

Example:
If today is 1 October 2015, an IBM bond pays $115 every September 30 for 5 years. In September 2020 it pays an additional $1000 and retires the bond. The bond is rated AAA (YTM is 7.5%).

Answer 12

r = 7.5% (YTM)
cpn = $115
par = $1000

Question 13

Example:
In Nov 2014 you purchase a 3 year US bond. The bond has an annual coupon rate of 4.25%, paid semiannually. If investors demand a 0.965% semi-annual return, what is the price of the bond?

Answer 13

Find the semi-annual coupon, find the semi-annual discount rate, and instead of x3 do x6 (because 6 half years == 3 years)

The semi-annual discount rate is:
Treasury bond has a yield to maturity of y, you have to remember to use y/2 as the semi-annual rate for discounting the cash flows

So in the example above, literally just half 0.965 –> 0.004825, and then do x6 instead of x3 as explained above

Question 14

What is the relationship between bond prices and yields?

Answer 14

Bond prices and yields must move in opposite directions. The yield to maturity, our measure of the interest rate on a bond, is defined as the discount rate that explains the bond price. When bond prices fall, interest rates (i.e., yields to maturity) must rise. When interest rates rise, bond prices must fall.

Question 15

What kind of bonds are more sensitive to change in interest rates?

Answer 15

Long term bonds

Question 16

If an interest rate of 8% means a bond sells at face value. What happens if the interest rate exceeds 8%?

Answer 16

Interest rate > Bond coupon (8%):
-> The bond sells at a discount (below face value), because the fixed coupon payments are LESS attractive that the higher interest rates.

Question 17

If an interest rate of 8% means a bond sells at face value. What happens if the interest rate is smaller than 8%?

Answer 17

Interest rate < Bond coupon (8%):
-> The bond sells at a premium (above face value), because the fixed coupon payments are MORE attractive that the higher interest rates.

Question 18

How do you calculate rate of return?

Answer 18

Rate of Return = Total income per period per dollar invested

Question 19

What is the duration/ Macaulay Duration?

Answer 19

Duration (or Macaulay Duration) is the weighted average of the times to each of the cash payments. These times represent the future years (1, 2, 3, etc.), extending to the final maturity date, referred to as T. A higher bond duration indicates a greater sensitivity to changes in interest rates.

Question 20

What is the relationship between short and long term interest rates called?

Answer 20

The relationship between short- and long-term interest rates is called the term structure of interest rates. Short- and long-term rates are not always parallel. Between September 1992–April 2000: U.S. short-term rates rose sharply while long-term rates declined.

Question 21

What is the spot rate?

Answer 21

The spot rate is the current interest rate for immediate transactions or loans (at time 𝑡 = 0). It represents the actual interest rate available today for a specific maturity.

Question 22

What is the future rate?

Answer 22

Future Rate: Spot rate expected in future

Question 23

What is the forward rate?

Answer 23

Interest rate, fixed today, on future loan at fixed time

Question 24

What are the 3 possible reasons for investing in a short-term bond which is rewarded with a lower rate than a longer-term bond?

Answer 24

• Investors might believe that short-term interest will be higher in the future
• Concerns about greater exposure of long-term bonds to changes in interest rates
• Concerns about the risk of future inflation

Question 25

What is important about the expectations theory (spot and forward rates)?

Answer 25

-> According to the Expectations Theory, the spot rate for a given maturity (the rate available today for that specific term) already reflects the average of all forward rates up to that maturity. Therefore, when you are discounting cash flows for a project with a particular term (e.g., a 5-year project), you should use the 5-year spot rate.

Question 26

What does arbitrage mean?

Answer 26

The technical term for money machine is arbitrage. Arbitrageurs are always on the look out for cases where two identical sets of future cash flows are selling at different prices. In well-functioning markets, where the costs of buying and selling are low, arbitrage opportunities are eliminated almost instantaneously by investors who try to take advantage of them.

Question 27

Why does the term structure of long term bonds slope upward?

Answer 27

Inflation is an important source of risk for long-term investors. Borrowers must offer some extra incentive if they want investors to lend long. That is why we often see a steeply upward sloping term structure when inflation is particularly uncertain.

Question 28

If inflation is present, will real interest rate be greater or smaller than nominal interest rate?

Answer 28

In the presence of inflation, an investors real interest rate is always less than the nominal interest rate

Question 29

How do you calculate the real rate of return?

Answer 29

nominal interest rate / inflation rate

Question 30

If you get quoted 10% by a bond dealer, that involves a nominal interest rate. Say the expected inflation rate is 6%, what is the real rate of return?

Answer 30

say you invest 1000, that grows to 1100 (+10% nominal), but this is then corrected by dividing 1100/ 1.06 (Due to the 6% inflation rate!)

Question 31

What is Fisher’s Theory?

Answer 31

A change in the expected inflation rate causes the same proportionate change in the nominal interest rate; it has no effect on the required real interest rate.

Question 32

What is important to remember about “Treasury Inflation-Protected Securities (TIPS)”?

Answer 32

The real cash flows on TIPS are fixed, but the nominal cash flows (interest and principal) increase as the CPI (inflation!) increases.
For example, suppose that the U.S. Treasury issues 3% 20 year TIPS at a price equal to its face value of $1,000. If during the first year the CPI rises by 10%, then the coupon payment on the bond increases by 10% from $30 to 30 × 1.10 = $33.16 The amount that you will be paid at maturity also increases to $1,000 × 1.10 = $1,100.

Question 33

What is “default risk”?

Answer 33

The risk that a bond issuer may default on its bonds

Question 34

What is “default premium”?

Answer 34

The additional yield on a bond that investors require for bearing credit risk

Question 35

What are “investment-grade bonds”?

Answer 35

Bonds rated Baa or above by Moody’s or BBB or above by Standard & Poor’s

Question 36

What are “junk bonds”?

Answer 36

Bond with a rating below Baa or BBB

Question 37

How big is the risk of a default really?

Answer 37

It is rare for highly rated bonds to default. However, when an investment-grade bond does go under, the shock waves are felt in all major financial centers. For example, in May 2001, WorldCom sold $11.8 billion of bonds with an investment-grade rating. About one year later, WorldCom filed for bankruptcy, and its bondholders lost more than 80% of their investment. For these bondholders, the agencies that had assigned investment-grade ratings were not the

Question 38

Why are yields on corporate bonds higher than government bond yields?

Answer 38

Because of the risk of default, yields on corporate bonds are higher than those of government bonds.

Question 39

What are key facts about “foreign currency debt”?

Answer 39

• Default occurs when foreign government borrows dollars
• If crisis occurs, governments may run out of taxing capacity and default
• Affects bond prices, yield to maturity

Question 40

What are key facts about “own currency debt”?

Answer 40

• Less risky than foreign currency debt
• Governments can print money to repay bonds
• Investors are subjected to local currency devaluation

Question 41

What are key facts about “eurozone debt”?

Answer 41

• Can’t print money to service domestic debts
• Money supply controlled by European CB